Payburner allows you to see the transactions on your XRP Account.  This view is enabled by default.

The long randomized text string underneath the XRP Balance is your XRP address.  Click on it to set it in your clipboard for copy paste.  Payments received will be marked in green.  Payments sent in red.

At any time, you can come back to this view, by clicking on the menu icon in the upper right and then on XRP Transactions.

By default, the XRP transactions created by Payburner to register your private keys are filtered.  Click on the Filter switch if you wish to see them.  For an explanation of these transactions, click on What are these weird micro payments I see when I turn off filtering ?.